MathSysProject:Modellinginformationpropagationthroughthemicrotubulelattice.Supervisors:Burroughs(MathematicsInstitute)&Cross(MedicalSchool)Background: Microtubules are bistable polymers that spontaneously switch betweenpolymerisation(lengthening)anddepolymerisation(shortening),abehaviourcalleddynamicinstability.Microtubulescomprise13protofilamentsthatarearrangedinatube,seeFigure1.Itwasuntilrecentlybelievedthatonceassembled,themicrotubuletubewasstatic,butrecentevidencerevealsthatitslatticeofsubunitsishighlydynamicandplasticandthatitcansense,integrate and transmit mechanical signals (information). We now know for example thatmicrotubules can self-repair and that the binding of interacting proteins to the latticemodulatesitsspacing,itscurvature,itsstabilityanditstendencytobindfurtherproteinsanddrugs[1,2].Wehypothesisethatproteinbindingexerts itseffectsbygeneratingmechanicalstress in the lattice.Thisstress thenpropagates throughthe lattice,changing itsproperties.As a result,microtubulemechanics,microtubule dynamic instability and themodulation ofthelatticebyproteinbindingareintertwined,havingacommondependenceonlatticestress.Thisprojectwillconstructa3Dsimulationofmicrotubulesinformedbyexperimentaldata, anddevelopadeepunderstandingofmicrotubulelatticemodulationandsignalpropagation.

Theproject:Youwillbuildasimulationmodelofamicrotubule,modellingthemicrotubuletube by a network of springs connecting the Tubulin dimers (the subunits that form themicrotubule lattice), Figure 1. Such models are called bead-spring models. Key will becapturing the microtubule’s natural anisotropy in the model, i.e. distinguishing thelongitudinal protofilament bonds and the lateral bonds between protofilaments to form anorthotropic tube model. The elasticity of an orthotropic tube depends on the direction ofstretch.Tubulindimersalsohaveanaturalbend,Figure1,soprotofilamentsarecurvedwhennot part of themicrotubule, and generate internal stresswithin the tube. Yourmodelwillcomprisebeads(Tubulindimers)connectedby6springswithspringconstants,orientationpotentialsthatconstrainthespringdirectionandforcedependentbondbreakingrates,Figure1. Parameters will be determined from experimental data where available, and otherwisedeterminedfromqualitativecomparisontoobservedbehaviour.You will analyse a number of experiments (with potential to constrain model parametersdirectlyfromdata):i) Microfluidic bending of microtubules. Microtubules bend under flow in microfluidicchambers.Byaddingbindingproteins,thatbendcanbefixed-inwhentheflowisstopped[1].

Fig.1 Lattice of spring-bonds model. Left: a microtubule composed of tubulin dimers organised into 13 protofilaments; the pitch of the spiral is such that there is a seam on one side. The panel shows the six bonds between dimers. Right: sketch of the bonds for Tu-GDP and Tu-GTP αβ dimers which have characteristically different spring bonds. Each bond has a length, a stiffness, a 3D directional preference (cones) and a strain-dependent breaking rate.

α

β

15o

Longitundinal spring bonds

radialdirection

Tu-GDP

α β

α β

α β

15oTu-GTP

Lateral spring bonds

Orientation compliance

along surface

protofilament axisprotofilament axis

Youwillreproducethisbehaviourfromyoursimulationandcomparetothebehaviourofanelasticrodmodel[3].Akeyunknownhereisthedegreeofclusteringduringbindingthatmayexplainthemicrotubulecrinklingobservedexperimentally.ii) Shearing ofmicrotubules. By bindingmicrotubules to a surface coated in amicrotubulebindingprotein, it isobservedduringdepolymerisation that the topof themicrotubulecanshearoffleavingapartialtube(tail),about½ofthetube[1].Youwillsimulatethisandfindparameterssetsthatreproducetheeffectwithrealisticrates(egmatchtailandtopretractionrates).iii) Bending and buckling of microtubules byforcesinadualbeamopticaltrap,Figure2.Theaim will be to reproduce the results of [4] onbuckling forces. You will compare to a simplerelastic rod model of microtubules [3] anddeterminetheerror inusing the latter.Youwillthen anlayse mechanical properties of baremicrotubulesandthosecoatedwithbindingproteins.Desirableskills.Youshouldhaveakeeninterestinusinghigh-levelcomputationalmethodsto solve problems. Programming is essential, ideally MatLab, C++ or python, althoughmoleculardynamicssimulators(e.g.LAMMPS)mayalsobeused ifdesired.ExperiencewithMontecarlomethodsand/oranunderstandingofmechanicswillbeuseful.PossibilitiesofaPhD.ThiscanbeextendedtoaPhDinanumberofwaysdependingontheinterestsofthestudent.Forinstance:i)APhDfocusingonstructuralchangesinthemicrotubulethroughproteinbinding.External:YouwouldcollaboratewithanexpertonMTcryoEMinBirkbeckCollege,ii)APhDfocusingondrugactionandhowdrugschangemicrotubulebehaviour.External:YouwouldcollaboratewithanexpertonMTdrugactioninGeneva.iii)APhDfocusingonmicrotubule latticedefects thatunderpinmicrotubule fatigue[5]andpossiblyrescueeventsindynamicinstability.External:YouwouldcollaboratewithanexpertonMTrepairandfatigueinCNRS,Grenoble,France.InthesePhDs,utilisingthelatestMontecarloalgorithmprotocols,suchasmulti-levelMC,andusingparallelisation,eitherMPI,GPUwouldbeakeyfocus.References.[1] Kinesin expands and stabilizes the GDP-microtubule lattice. R. Peet, Nigel J Burroughs,RobertA.Cross.NatureNanotechnology2018,13:386–91.[2] Kinesin-binding–triggered conformation switching of microtubules contributes topolarizedtransport.TomohiroShima,ManatsuMorikawa, JunichiKaneshiroetal.2018. JCB217,4164-83.[3]Curvature-SensitiveKinesinBindingCanExplainMicrotubuleRingFormationandRevealsChaoticDynamicsinaMathematicalModel.SimonP.Pearce,MatthiasHeil,GarethWynJones,AndreasProkop.BullMathBiol.2018.[4] Microtubules soften due to cross- sectional flattening. Edvin Memet, Feodor Hilitski,MargaretAMorrisetal.2018.eLife20187:e346695.[5] Microtubules self-repair in response to mechanical stress. Laura Schaedel, Karin John,Jérémie Gaillard,Maxence V. Nachury, Laurent Blanchoin, andManuel Théry. 2015.Naturematerials.14;1156-63.

Fig.2 Dual beam optical trapping

Trap1

Kinesin

BeadsTrap2